This the first in a series of papers whose ultimate goal is to establish the full nonlinear stability of the Kerr family for | a| ≪ m. The paper builds on the strategy laid out in  in the context of the nonlinear stability of Schwarzschild for axially symmetric polarized perturbations. In fact the central idea of  was the introduction and construction of generally covariant modulated (GCM) spheres on which specific geometric quantities take Schwarzschildian values. This was made possible by taking into account the full general covariance of the Einstein vacuum equations. The goal of this, and its companion paper , is to get rid of the symmetry restriction in the construction of GCM spheres in  and thus remove an essential obstruction in extending the result to a full stability proof of the Kerr family.
All Science Journal Classification (ASJC) codes
- Mathematical Physics
- Physics and Astronomy(all)
- Geometry and Topology
- Applied Mathematics